Leandro F. Aurichi

Topological games and Alster spaces

In this paper we study connections between topological games such as Rothberger, Menger and compact-open, and relate these games to properties involving covers by G_{delta} subsets. The results include: (1) If Two has a winning strategy in the Menger game on a regular space X, then X is an Alster space. (2) If Two has a winning strategy in the Rothberger game on a topological space X, then the G_delta-topology on X is Lindelof. (3) The Menger game and the compact-open game are (consistently) not dual.

A definitive improvement of a game-theoretic bound and the long tightness game

The main goal of the paper is the full proof of a cardinal inequality for a space with points

Topological games and productively countably tight spaces

{G_delta }

On a game theoretic cardinality bound

Gδ, obtained with the help of a long version of the Menger game. This result, which improves a similar one of Scheepers and Tall, was already established by the authors under the Continuum Hypothesis. The paper is completed by few remarks on a long version of the tightness game.